On strictly ergodic models for commuting ergodic transformations
type: Item
instance of: scholarly article
title: On strictly ergodic models for commuting ergodic transformations
zbMATH Open document ID: 0662.28009
author: S. H. Smith
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77340
review text: \textit{B. Weiss} [Bull. Am. Math. Soc., New Ser. 13, 143-146 (1985; Zbl 0615.28012)] proved that every ergodic \({\mathbb{Z}}^ 2\)-action has a strictly ergodic model. We strengthen this result in the following way: If the \({\mathbb{Z}}^ 2\)-action is ergodic and is generated by two commuting transformations S and T, there exists a strictly ergodic model in which every ergodic \({\mathbb{Z}}\)-action generated by some \(S^ iT^ j\) is itself strictly ergodic.
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 4081884
zbMATH Keywords: Rohlin tower
zbMATH Keywords: uniform partition
zbMATH Keywords: ergodic \({\mathbb{Z}}^ 2\)-action
zbMATH Keywords: strictly ergodic model
zbMATH Keywords: commuting transformations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4081884